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    GNSS/IMU Integration for Robustness/Accuracy

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    Technical Training Short On Site Course Quote

    This four-day course provides extensive coverage of multisensor integration by flight-validated methods. The instructor is the author of innovations in carrier phase, integrity, inertial error propagation (Matlab program for long term, commonality with tracking for short-term), and practical estimation techniques. It can benefit anyone involved in GNSS, inertial navigation or tracking, or any integrated combination.

    Motivation was prompted by vulnerability jamming and spoofing in current operations, drawing urgent attention toward robustness in satellite navigation (GNSS). Primary attention is given to GNSS (satellite) and inertial navigation, either used separately or together, with additional sensors (e.g., magnetometer, radar) also included. Both navigation and tracking of external objects are addressed, illuminating similarities and differences among applications.

    Most operations don't require pinpoint instantaneous location in minuscule volumes, but dynamic accuracy remains crucial (e.g., projecting over a minute ahead for collision avoidance). Prudence then urges precision in dynamics while accepting adequate position without laborious efforts vulnerable to catastrophic errors. The goal is met through sequential differencing of carrier phase and separate correction with pseudorange measurements, all subjected to rigorously derived integrity testing. Tight integration only begins to describe the approach.

    The course begins with fundamentals, showing clear intuitive connection of mathematics to physical examples, followed by a natural transition to advanced material. Practical realities are given top priority, by delivering maximum effectiveness from the simplest permissible representations. Optional exercises can therefore use almost any version of Matlab from within the past ten years. Instructor:

    James L. Farrell, Ph.D. is a former ION Air Nav Representative, a senior member of IEEE, a former local board member of AIAA, and a registered professional engineer in Maryland. Technical experience includes teaching appointments at Marquette and UCLA, two years each at Minneapolis Honeywell and Bendix-Pacific, plus 31 years at Westinghouse in design, simulation, and validation/test for modern estimation algorithms in navigation and tracking applications. He is author of INTEGRATED AIRCRAFT NAVIGATION and of GNSS AIDED NAVIGATION AND TRACKING (2007), as well as chapters in books edited by C.T. Leondes and Cary Spitzer. He was a columnist for WASHINGTON TECHNOLOGY, and has written over a hundred journal and conference manuscripts. Active in RTCA (Washington D.C.) for the past several years, he served as co-chairman of Working Group #5 (Fault Detection and Isolation) within Special Committee SC-159 for GPS Integrity. He has continued his teaching (on University campus as well as in both industry and conference seminars), while consulting for private industry, DOD, and University research.

    Contact this instructor (please mention course name in the subject line)

    What You Will Learn:

    • to prepare and integrate raw GNSS measurements (pseudorange and carrier phase, with raw data adhering to a different time base (from gyros, accelerometers, magnetometers)
    • to achieve state-of-the-art performance from low-cost equipment, counteracting long-term drifts
    • to follow direct step-by-step procedures, leaving you with entirely new depth of understanding closed form solution for inertial error propagation, tilt and velocity errors; intuitive results for durations up to a tenth Schuler period
    • analytical characterization for average rate of drift from pseudoconing,
    • an extensive array of motion-sensitive errors for gyros and accelerometers, including rectification effects
    • dramatic simplification of inertial error propagation and in Kalman filter models
    • commonality of short-term INS error propagation with simple track formulation
    • carrier phase benefits including elimination of all problems involving integer ambiguity and interoperability
    • description of FFT-based GPS processing and major benefits it offer
    • multiple advancements in RAIM including independent extension to each separate measurement tracking application
    • extensive description of related operations (transfer alignment, SAR motion compensation, etc.)

    Course Outline:

    1. Basic motion
      • 2-D and 3-D position, velocity, acceleration
      • Absolute and relative motions
      • Coordinate frames of interest
      • Misorientation
      • Euler angles, direction cosines, and quaternions
    2. Matrix math
      • Summations and simultaneous equations
      • Physical and probabilistic representations
      • Complex dynamics reduced t
      • intuitive form
    3. Further properties of motion
      • Rotational (gimbal lock)
      • Coupled translation/rotation
      • Gravitation vs gravity over a spheroidal earth
      • Vibration and its ramifications
    4. Inertial nav fundamentals
      • Mechanical and computational stabilization of platforms
      • Space stable and geographic references
      • Specific force from accelerometers
      • Absolute angular rate from gyros
      • Velocity and attitude from processing of increments
    5. Further Inertial nav issues
      • Leveling
      • Gyrocompassing
      • Coning and sculling
      • Motion-sensitive degradations
    6. IMU role in aiding; beginnings of integration
      • Uncoupled vertical channel
      • Schuler and short-term error propagation solutions
      • Wander azimuth
    7. Estimation
      • Fundamentals and definitions
      • KF, EKF, block vs recursion
      • Penrose, augmentation
      • 1-state and 2-state examples
      • Bierman UD factorization
    8. Observability
      • General block diagram
      • Subtle ramifications of c
      • -variances
      • State minimization
      • Model fidelity
      • Suboptimal: when and when NOT
    9. Span of influential updates
      • Data window
      • MATLAB program for illustration
      • Consequences of violation
      • Un-observability and false observability
    10. Navigation with GNSS data
      • From ICD message t
      • SV position & velocity
      • Pseud
      • -range and carrier phase
      • Backup t
      • transmit time
      • Classical 4-SV solution
      • Extensions
    11. Differencing
      • Across receivers, SVs, and time
      • Correlations introduced
      • MATLAB pre-whitening algorithms
    12. Integrity
      • Classical FDI/FDE
      • Extended RAIM
      • Single-measurement RAIM
      • Residual monitoring
      • Outlier editing in real time
    13. GNSS/Inertial integration
      • Conventional (pre-GPS) form
      • Low cost for avoidance of overdesign
      • Loose, tight, ultra-tight, deep
      • Pivotal value of Morrison insight
      • Dramatic simplification of dynamics
    14. 1-sec changes in carrier phase
      • Advantage over delta range/Doppler/delayed states
      • Formation of residuals
      • Formation of sensitivities
    15. Robust configuration: Segmented GNSS/IMU
      • Block diagrams, symbolic and detailed
      • Long list of robustness features
      • Rationale for precision in dynamics only
      • Extension t
      • precise positioning
    16. Tracking
      • 6-state, 7-state, 9-state
      • Channel separation: when and when NOT
      • Mitigation of nonlinearities
      • Concurrent stabilization
    17. Tracking Application similarities and differences
      • Projectile
      • Orbit determination
      • Re-entry vehicle
      • TWS littoral surveillance
    18. Illustrative Applications
      • Transfer alignment
      • SAR motion compensation
      • Mutual Surveillance
      • Collision avoidance
      • Cooperative Engagement
    19. Experimental results
      • Sparse data with and without cueing
      • Decimeter/sec in flight without IMU
      • cm/sec in flight with IMU
    20. Practical issues
      • Processing of magnetic heading data
      • Coordination of simulation, test, real-time operation
      • MATLAB program for long term coast
    21. Trends
      • Extended coast durations (welcome back, 1970!)
      • Beware of aliasing; MATLAB program example
      • Classical/Current/Future Integration
    22. Extended operation
      • Additional sensors (air data, Doppler, DME, eLoran, r-f, vision, terrain or mag patterns)
      • Support of additional processes (interferometry, conformal arrays, beamforming, null steering)
      • Additional applications (UAV, UWV, driverless cars, etc.)


    This course is not on the current schedule of open enrollment courses. If you are interested in attending this or another course as open enrollment, please contact us at (410) 956-8805 or at and indicate the course name and number of students who wish to participate. ATI typically schedules courses with a lead time of 3-5 months. Group courses can be presented at your facility. For on-site pricing, request an on-site quote. You may also call us at (410) 956-8805 or email us at